The ability to accurately and controllably reduce vibration, and to otherwise precisely control motion, is a coveted capability useful in governing the behavior of a wide variety of manufacturing processes and equipment. For example, it is well-known that semiconductor capital equipment, such as lithography stages, laser light sources, metrology stages, pick-and place-equipment and wafer-handling robots, must operate within specifically calibrated, relatively fault-intolerant operational ranges of movement and other physical conditions. Beyond these ranges, the products produced by such equipment, and the equipment itself, may be defective or nonfunctional.
Indeed, semiconductor chip manufacture can be so sensitive, that tiny ranges of unwanted motion, for example, in the micrometer (μm) to nanometer (nm) range, can interfere with components or subsystems that require precise alignment and positioning. The need for such near-exacting precision in chip manufacturing is illustrated, for instance, in the careful matching of a wafer mask to a silicon substrate. Because, in this context, small variances in mask placement may escape detection until the quality control inspection, or worse, until installation in end-products, the need for identifying and quickly correcting the effect of positioning and disturbance-related errors in the first place is of utmost importance.
As chip-making technology has advanced, for example, through the use of advanced photolithography lasers such as those sold by Cymer, Inc. of San Diego, Calif., chip throughput requirements have also increased. One consequence of the increased requirements has been a larger positioning bandwidth of photolithography stages. However, with greater bandwidth has come increases in the attendant motion or stage control issues. For example, among other effects upon manufacturing, the increase in positioning bandwidth has implicated the need to predict and control flexible deformation modes of stages into the control band of the system. This, coupled with the typical stage's relatively low level of structural damping (arising from the requirement that the stages be both light and stiff), creates a host of scenarios where the stage must be carefully controlled to achieve sustained, near-optimal operational behavior. Here again, the need for highly precise control is keenly felt.
Any control system used in such situations should ideally be capable of tuning itself to maximize system performance in the presence of these variations. Also, since optimality of the control system is dependent on magnitude, frequency response, and other characteristics of system disturbances, the control system preferably should notice, adjust and, if necessary, compensate for and overcome unwanted effects of the disturbances.
Active vibration and motion control provides one promising method of achieving adequate system governance. Active control is often a suitable technology for dealing with vibration and motion control issues for a number of reasons, such as those discussed in commonly-owned U.S. Ser. No. 09/491,969, which is hereby incorporated by reference. However, unknowns in plant dynamics and unforeseen disturbances to the system being controlled can significantly alter the actual results attained through active structural control, especially when used with sensitive machines such as semiconductor capital equipment. In this context, disturbances can manifest themselves in a variety of ways, such as affecting the signals input to the system being controlled, causing variances in sensor signals or by impacting performance variables. In addition, uncertainty in stage dynamics, and the impact upon those dynamics caused by changes in equipment configuration, mass distribution, and aging of equipment, subsystems, or components, all may serve to limit the performance of any standard control method chosen.
The shortcomings of active control are especially appreciated when taken from a predictable laboratory setting to the rigors of the factory floor. In laboratory tests, one can characterize the system being controlled, including experimentally induced disturbances, before closing the loops and then adjust the control gains to get the best possible response out of the system. In this manner, it is possible to eliminate much of the uncertainty about a system's input/output behavior in a specified frequency range, especially when using modern system identification techniques. In real world applications, however, it is more difficult to recreate system performance identical to that observed in the lab. Part-to-part variation results in differences in response to control inputs, even between nominally identical systems, and even when using the same controller. Changes in environment and equipment configuration can cause sometimes difficult to pinpoint modeling errors because they can vary from location to location and may also vary with time. These issues often arise in the case of semiconductor fabrication equipment, where the dynamics of the individual system may not be completely known until it has been deployed and used in the factory. Furthermore, the exact character of a disturbance in physical conditions, let alone specific disturbance frequencies, may not be known ahead of time with the precision needed to optimize performance and can be time-varying themselves.
Researchers have been addressing these issues outside of the semiconductor industry by applying adaptive control techniques to the structural control problem. The thrust of these efforts has been to make the adaptive control algorithms as general as possible, with the goal of making a controller which uses an unchanging theoretical model to work for all conceivable systems under all conditions. Such an ideal controller usually is necessarily (and undesirably) complex for most practical applications and, in use, may limit the performance of the controller. In addition, if the model of the plant changes as a function of time, the performance of the controller may be limited if these changes are not captured in the model.
Some research in the area of adaptive control has focused on its application to flexible structures. Roughly, the favored approaches of these efforts can be divided into three classes of feedback control: direct adaptive control, self tuning regulators, and tonal controllers. The direct adaptive controllers compute control gains “adaptively”, i.e., directly from measurement errors. In general, these types of controllers guarantee stability via Lyapunov theory. However, direct controllers usually require that actuators and sensors be collocated and dual to enforce a positive real condition in the transfer functions. In practice, it is often difficult to construct sensor/actuator pairs that yield truly positive real behavior. Either non-idealities, such as amplifier dynamics, violate the condition, or the collocation of actuators and sensors forces an unsatisfactory reduction in closed-loop performance.
Tonal controllers are those designed to perform disturbance rejection at one or several discrete frequencies. The disturbance is usually a sinusoid, usually of unknown frequency. The tonal controller typically either adapts to changes in frequency, changes in plant dynamics, or both. This type of control can achieve perfect disturbance rejection (even in non-positive-real systems) in instances where the number of error sensors is less than or equal to the number of actuators and the actuators have sufficient control authority. Self tuning regulators add an extra step to the adaptation process, namely, the adaptive updating of an internal model in the tuning algorithm. This model is used to compute control gains. These methods generally do not require collocation, and are distinguished from each other primarily by the algorithm used to perform identification (ID) of the internal model. Among the ID methods used in these types of controllers are neural nets, modal parameters, physical structural properties (e.g. mass and stiffness) and families of models that span the parameter variation space.
Generally, existing self tuning regulators exhibit several shortcomings that hamper their utility. For example, existing regulators update the controller (and the internal model associated therewith) at each controller cycle. As such, the computations required to ensure stability of the controller's operation are complex and burdensome. In application, there are times when these computations cannot be adequately performed during each controller cycle, such as when the equipment being regulated demands relatively high bandwidth control. In addition, because the equipment being regulated is in operation i.e., “normal use,” while tuning data is acquired, it is undesirable and, sometimes impossible, to inject any alternative “test” actuation signals into the system; thus, any self tuning is solely dependent upon the existing operating signals. The result is that there are times where these operating signals do not adequately excite the dynamics of the plant to a level necessary to obtain a high fidelity model of the plant dynamics. Since a controller, to some degree, is only as good as the plant model upon which it depends, model fidelity can directly limit the performance of the controller. Thus, in order to better characterize the plant, the ability to introduce an alternative excitation signal would be desirable.
Attempting to tune controller parameters during system operation is an additional layer of complexity that is frequently excessive and unnecessary to most manufacturing applications. Indeed, many of the advantages of adaptive control, without the limitations imposed by non-linear stability requirements, can be realized by occasionally taking a manufacturing machine off-line i.e., “abnormal use,” to gather system data and tune the controller parameters based on the new data. This concept of tuning control parameters at infrequent intervals to improve performance of feedback control systems has been implemented in the context of tuning a proportional plus-integral-plus-derivative (PID) controller. Recent work extends PID auto-tuning concepts to multivariable systems, albeit systems with a few degrees of freedom or states, usually only suitable for measuring a maximum of three parameters: frequency, amplitude, and phase of a signal. Since only three parameters are measured, it is only possible to modify a controller for a system that is a second order (or lower) dynamic system. This constraint hampers the usefulness of this method.
Moreover, it is typically only possible to apply this method to single-input, single-output PID controllers, making it poorly suited for dynamically complex multi-input, multi-output systems typical of semiconductor manufacturing equipment. Manufacturing equipment often requires more than about 16, and sometimes as many as 32 or more, states to accurately model the system and to control it adequately. Other work has extended the concept to multivariable systems, and employs the use of non-linear curve fitting to match models to frequency response measurements. That work, however, has been generally limited to large flexible structures, such as spacecraft, and used several very high powered computers, including a Cray supercomputer, to implement the algorithms. Also, it assumed that transfer functions from disturbances and from actuators to performance variables could be measured. In addition, the prior work required the creation of unique mathematical filters for every given system configuration, which in turn required the services of a computer programmer to effectively create new software unique to any given control situation. As a result, prior attempts to tune control parameters in an off-line scenario have required large amounts of experimental data and significant amounts of processing time at uncommon processing speeds to achieve results. Such methods, using specialized equipment and expertise, proves to be impractical in a typical manufacturing setting for all but the most time- and cost-insensitive applications.
Other prior systems and methods further demonstrate the need for a practical, novel approach to self-tuning regulators. For example, tuning of a portion of a control system is practiced by McConnell et al. in U.S. Pat. Nos. 6,011,373 and 6,002,232, and Singer, et al. in U.S. Pat. No. 4,916,635. However, the adjustment performed is considered to be command shaping. In these scenarios, adjustment of the input commands is performed rather than adjustment of the feedback controller used to regulate the operation of the system. This adjustment to the input command is in response to errors measured from previous input commands. The disadvantage of this method is that it does not address external disturbances.
McConnell et al. discloses the use of time domain measurements to update a single input, single output open loop controller in U.S. Pat. No. 5,594,309. However, this system only provides for adjustment of the input filter used to command the point-to-point movement of the system. It does not provide for adjustment of the controller to account for external disturbances or for trajectory following. Dickerson et al. discloses a form of input command adjustment in U.S. Pat. No. 5,946,449, which closely parallels the adjustment performed by Dickerson et al.
In U.S. Pat. No. 6,076,951, Wang et al. disclose a system that employs relay feedback or step input, where a linear least squares curve fit is employed to derive the desired controller. In this case, a direct inversion of the desired closed loop performance is conducted. The controller structure and gains are derived directly from a system identification fit of the closed loop performance using a polynomial parameterization of the control. This method has poor numeric conditioning and, as such, usually will not converge to the correct model for large order (i.e., greater than 10 states) systems. In addition, the use of a step or relay input to the system does not always provide enough information about the dynamic behavior of the plant.
WO 00/41043 by Tan et al. discloses a system that provides for adjustment of gain values for a PI controller using time domain data to determine how to adjust the system. This disclosure does not address updating of model parameters, but rather, requires that the model be known. As such, the performance of the system is not robust to variations in the plant.